RE Microsoft Word: last I heard they use regular expressions or something similar, so I wouldn’t expect it to do great when there’s an interaction of number agreement with coordination. Their translation team has some grammar-based parsers but I don’t know if the Office team uses them, or if they even model agreement any better.

I also have little objection to Where is the key and the book? and even less with the contraction Where’s. Where are the key and the book? sounds almost pedantic in an informal register, but I also know better (when I notice it) when speaking/writing more formally. I would appreciate a model of standard English grammar to tell me when I’ve made such a mistake, and I think that’s part of the “policy” with the ERG: it should say when something is grammatical or not and not just provide a best guess when something isn’t. But it also reflects modern usage in some respects, such as This data shows us nothing parses but These data show us nothing does not. Sometimes it accommodates regional variation, such as The government is incompetent and The government are incompetent; both parse, but both also have NUM: sg on _government_n_of.

If you want to parse things that are a little ungrammatical, you can try using a version of the ERG with “mal-rules”. I’m not sure which configuration is best, but when I compile the ERG with it’s ace/config-educ.tdl configuration, I’m able to get a parse for Where is the key and the lock?.

The grammar aims to reflect modern usage in edited text, with some accommodation for the inevitably blurry edges. I have not yet come around to “Where is the key and the book?” which sounds wrong to me, but may well be on its way to standard usage eventually, and I agree that it’s better with the contracted auxiliary. The analogous pair with “There” sounds much better even to me, and both are already analyzed as fine in the grammar: “There is/'s a key and a book on the table.”
But yes, you might experiment with the variant of the grammar used in teaching English, which relaxes some of the constraints that hold for edited English, while mostly still preserving the MRS that would have been produced by the well-formed variant of the error-bearing sentence. The potential drawback in using that version is that you get even more ambiguity, and the parse ranking model currently knows nothing about those relaxed rules, so I’m doubtful that it will serve your needs. I will be interested to know if you run into many of those edge-of-grammaticality examples in your application.